| Hawking Temperature |
Article Index for Hawking |
Website Links For Hawking |
Information AboutHawking Temperature |
| CATEGORIES ABOUT HAWKING RADIATION | |
| black holes | |
| quantum field theory | |
|
Hawking's discovery became the first convincing insight into Quantum Gravity . However, the existence of Hawking radiation remains controversial. Los Alamos National Laboratory (Archives) - "Do black holes radiate?" OVERVIEW Black Holes are sites of immense Gravitational Attraction into which surrounding Matter is drawn by gravitational forces. Classically, the gravitation is so powerful that nothing, not even Radiation or light, can escape from the black hole. It is yet unknown how Gravity can be incorporated into Quantum Mechanics , but nevertheless far from the black hole the gravitational effects can be weak enough that calculations can be reliably performed in the framework of Quantum Field Theory In Curved Spacetime . Hawking showed that quantum effects allow Black Holes to emit exact Black Body Radiation , which is the average thermal radiation emitted by an idealized thermal source known as a Black Body . The Radiation is as if it is emitted by a Black Body of Temperature which is related ( Inverse Proportional ) to the Black Hole 's Mass . Physical insight on the process may be gained by imagining that Particle - Antiparticle radiation is emitted from just beyond the Event Horizon . This radiation does not come directly from the black hole itself, but rather is a result of Virtual Particle s being "boosted" by the black hole's gravitation into becoming real particles. A more precise, but still much simplified view of the process is that Vacuum Fluctuations cause a particle-antiparticle pair to appear close to the Event Horizon of a black hole. One of the pair falls into the black hole whilst the other escapes. In order to preserve total Energy , the particle which fell into the black hole must have had a negative energy (with respect to an observer far away from the black hole). By this process the black hole loses mass, and to an outside observer it would appear that the black hole has just emitted a Particle . An important difference between the Black Hole Radiation as computed by Hawking and a Thermal Radiation emitted from a Black Body is that the latter is statistical in nature, and only its average satisfies what is known as Planck's Law Of Black Body Radiation , while the former satisfies this law ''exactly''. Thus Thermal Radiation contains Information about the body that emitted it, while Hawking radiation seems to contain no such information, and depends only on the Mass , Angular Momentum and Charge of the black hole. This leads to the Black Hole Information Paradox . However, according to the conjectured Gauge-gravity Duality (also known as the AdS/CFT Correspondence ), black holes in certain cases (and perhaps in general) are equivalent to solutions of Quantum Field Theory at a non-zero Temperature . This means that no information loss is expected in black holes (since no such loss exists in the Quantum Field Theory ), and the radiation emitted by a black hole is probably a usual thermal radiation. If this is correct, then Hawking's original computation should be corrected, though it is not known how (see Below ). = An example A Black Hole of one Solar Mass has a temperature of only 60 nanokelvin; in fact, such a black hole would absorb far more Cosmic Microwave Background Radiation than it emits. A black hole of 4.5 × 10&2&2 kg (about the mass of the Moon ) would be in equilibrium at 2.7 kelvins, absorbing as much radiation as it emits. Yet smaller Primordial Black Hole s would emit more than they absorb, and thereby lose mass. Problems with the theory The Trans-Planckian Problem may raise doubts on the physical validity of Hawking's result. Hawking's original derivation employed field modes of arbitrarily high frequency near the black hole horizon, although these do not appear in the final result. In particular, he used modes of frequency higher than the inverse Planck Time , and at these scales the physical laws are unknown. A number of alternative approaches to the Hawking radiation have appeared in order to try to overcome or address this problem. Some of these are in connection with the Unruh Effect . The Hawking Radiation shows that the laws of Black Hole Thermodynamics have a complete physical meaning. EMISSION PROCESS A black hole emits thermal radiation at a Temperature :, in Natural Units with ''G'', ''c'', and ''k'' equal to 1, and where is the Surface Gravity of the horizon. In particular, the radiation from a Schwarzschild black hole is Black-body Radiation with temperature: : where is the Reduced Planck Constant , ''c'' is the Speed Of Light , ''k'' is the Boltzmann Constant , ''G'' is the Gravitational Constant , and ''M'' is the Mass of the black hole. BLACK HOLE EVAPORATION When particles escape, the black hole loses a small amount of its energy and therefore of its mass (recall that mass and energy are related by Einstein's Famous Equation '' E = Mc&2 ''). The Power emitted by a black hole in the form of Hawking radiation can easily be estimated for the simplest case of a nonrotating, non-charged Schwarzschild Black Hole of mass ''M''. Combining the formulae for the Schwarzschild Radius of the black hole, the Stefan-Boltzmann Law of black-body radiation, the above formula for the temperature of the radiation, and the formula for the surface area of a Sphere (the black hole's Event Horizon ) we get: : where ''P'' is the energy outflow, '''' is the Reduced Planck Constant , ''c'' is the Speed Of Light , and ''G'' is the Gravitational Constant . It is worth mentioning that the above formula has not yet been derived in the framework of Semiclassical Gravity . The power in the Hawking radiation from a Solar Mass black hole turns out to be a minuscule 10−28 watts. It is indeed an extremely good approximation to call such an object 'black'. Under the assumption of an otherwise empty universe, so that no Matter or Cosmic Microwave Background Radiation falls into the black hole, it is possible to calculate how long it would take for the black hole to evaporate. The black hole's mass is now a function ''M''(''t'') of time ''t''. The time that the black hole takes to evaporate is: : For a black hole of one solar mass (about 21030 kg), we get an evaporation time of 1067 years—much longer than the current Age Of The Universe . But for a black hole of 1011 kg, the evaporation time is about 3 billion years. This is why some astronomers are searching for signs of exploding Primordial Black Holes . In common units, : : : So, for instance, a 1 second-lived black hole has a mass of 2.28 × 105 kg, equivalent to an energy of 2.05 × 1022 J that could be released by 5 × 106 Megatons Of TNT . The initial power is 6.84 × 1021 W. Black hole evaporation has several significant consequences:
HAWKING RADIATION AND LARGE EXTRA DIMENSIONS Formulas from the previous section are only applicable if laws of gravity are approximately valid all the way down to the Planck scale. In particular, for black holes with masses below Planck mass ( ~10-5 g ), they result in unphysical lifetimes below Planck time ( ~10-43 s ). This is normally seen as an indication that Planck mass is the lower limit on the mass of a black hole. In the model with Large Extra Dimension s, values of Planck constants can be radically different, and formulas for Hawking radiation have to be modified as well. In particular, the lifetime of a micro black hole ( with radius below the scale of extra dimensions ) is given by
DEVIATION FROM HAWKING RADIATION IN LOOP QUANTUM GRAVITY A detailed study of the quantum geometry of a black hole horizon has been made using Loop Quantum Gravity . Loop-quantization reproduces the result for Black Hole Entropy originally discovered by Bekenstein and Hawking . Further, it led to the computation of quantum gravity corrections to the entropy and radiation of black holes. Based on the fluctuations of the horizon area, a quantum black hole exhibits deviations from the Hawking spectrum that would be observable were X-ray s from Hawking radiation of evaporating Primordial Black Holes to be observed. The deviation is such that the Hawking radiation is expected to be centered at a set of discrete and unblended energies. REFERENCES
NOTES SEE ALSO
EXTERNAL LINKS
|
|
|